The torpedo is a nonlinear object which is very difficult to control. Via to manage the rudder angle yaw, the diving plane angle, and the fin shake reduction, the torpedo yaw horizontal, the depth vertical and roll damping of the system are controlled accurately and steadily. In this paper, the particle swarm optimization is used to correct the imprecision of architecture fuzzy parameters. The coverage width of membership function and the overlap degree influence of neighboring membership functions are considered in the method to adjust dynamically from the system errors. Thereby optimizing the control signal and enhancing the torpedo motion quality. The proposed method results in a better performance compared to the other control method such as adaptive fuzzy-neural that proved effective of the proposed controller.

1. TELKOMNIKA, Vol.16, No.6, December 2018, pp.2999~3007
ISSN: 1693-6930, accredited First Grade by Kemenristekdikti, Decree No: 21/E/KPT/2018
DOI: 10.12928/TELKOMNIKA.v16i6.8979  2999
Received March 20, 2018; Revised October 3, 2018; Accepted October 30, 2018
Optimal Control for Torpedo Motion based on
Fuzzy-PSO Advantage Technical
Viet-Dung Do*1
, Xuan-Kien Dang2
1
Ho Chi Minh City University of Transport and Dong An Polytechnic, Vietnam
2
Ho Chi Minh City University of Transport, Vietnam
*Corresponding author, e-mail: dangxuankien@hcmutrans.edu.vn
Abstract
The torpedo is a nonlinear object which is very difficult to control. Via to manage the rudder angle
yaw, the diving plane angle, and the fin shake reduction, the torpedo yaw horizontal, the depth vertical and
roll damping of the system are controlled accurately and steadily. In this paper, the particle swarm
optimization is used to correct the imprecision of architecture fuzzy parameters. The coverage width of
membership function and the overlap degree influence of neighboring membership functions are
considered in the method to adjust dynamically from the system errors. Thereby optimizing the control
signal and enhancing the torpedo motion quality. The proposed method results in a better performance
compared to the other control method such as adaptive fuzzy-neural that proved effective of the proposed
controller.
Keywords: fuzzy controller, particle swarm optimization, neighboring membership functions, nonlinear
object, torpedo motion
Copyright © 2018 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
The torpedo motion is a nonlinear and complicated in practical applications. The
torpedo actuator system executes control commands to ensure that object sponges the
reference trajectory. The accurate and steady control of torpedo is very difficult for its internal
nonlinear characteristics, uncertain architecture cofficients and disturbances. A Faruq et al.
(2011) present the fuzzy algorithm combined with the output gain optimization algorithm to
improve the response quality as well as the weight update time of the controller [1]. C Vuilmet
(2006) introduces a solution that combines a back stepping algorithm with accelerometer
feedback technology to control a torpedo, sponge a preset trajectory by the navigation system
[2]. This solution shows promising results on the realistic simulations, including highly time-
varying ocean currents. Thereby, the environmental impact has a significant effects on the
torpedo trajectory. The other study, U Adeel et al. design a sliding mode controller to aim the
stable robustness of heavy-weight torpedo [3]. It is impressed that the performance of state
feedback control is recovered arbitrarily fast by the proposed output feedback controller in the
parametric uncertainties, and the sea current perturbation due to flow effects as well as tides. In
order to improve the effective of sliding mode controller, D Qi et al. propose a hybrid fuzzy
sliding mode control strategy. The fuzzy rules were adopted to estimate the disturbance terms
[4]. But the fuzzy membership function that is estimated by programmer experiment are not able
to provide an effective approach for nonlinear systems. The direct adaptive
fuzzy-neural output feedback controller (DAFNOC) is proposed by V P Pham et al. which uses
the fuzzy neural network singleton to approximate functions and calculate the control law with
on-line turning weighting factors of the controller functions [5]. Simulation results show that the
system is able to adapt to external disturbance and interference evaluation of control channels.
Hierarchical fuzzy structure fit out an effective method approach for torpedo nonlinear
systems due to the fuzzy system ability to approximate a nonlinear composition. In this paper,
the authors have been proposed fuzzy particle swarm optimization (FPSO) advantage control
technical for torpedo motion optimization. Particle swarm optimization (PSO) is adopted to
calibrate the structure of fuzzy controller, thereby enhancing the quality of system and
optimizing the controller structure for torpedo motion. On the other hand, the proposed method

2.  ISSN: 1693-6930
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can be carried out for the other kind of autonomous underwater vehicles (AUVs) or applied in
ship control.
The paper is organized as follows. Section 2 presents the torpedo mathematical model.
The FPSO advantage control technical for torpedo motion optimization is proposed in section 3.
Section 4 provides simulations, the results are discussed. The conclusion is given in section 5.
2. Torpedo Models
The dynamic model of AUV [6, 7] which is presented by T I Fossen shown as in
Figure 1. Torpedo motion is described by six-degree of freedom, the centre of mass coincide
with the centre of gravity 𝐺 𝑏. Physical quantities include force, torque, velocity and angular
velocity of the torpedo coordinate system which are denoted by: 𝜏1 = [𝑋, 𝑌, 𝑍] 𝑇
is an external
force vector that have an effect on the torpedo; 𝜏2 = [𝐾, 𝑀, 𝑁] 𝑇
is an external force vector;
𝜏1 = [𝑈, 𝑉, 𝑊] 𝑇
is a linear velocity vector along the longitudinal of 𝑋 𝑏, 𝑌𝑏, 𝑍 𝑏 coordinate axes;
𝜔 = [𝑝, 𝑞, 𝑟] 𝑇
is the angular velocity vector of the rotating frame; 𝑣 = [𝑢, 𝑣, 𝑤, 𝑝, 𝑞, 𝑟] 𝑇
is the linear
velocity vector of rotating frame.
Figure 1. Inertial frame and body-fixed frame of torpedo
The positions 𝑥, 𝑦, 𝑧 and 𝜑, 𝜕, 𝜓 orientation angles of torpedo are expressed by:
𝜂 = [𝜂1
𝑇
, 𝜂2
𝑇
] 𝑇 (1)
where 𝜂1 = [𝑥, 𝑦, 𝑧] 𝑇
and 𝜂2 = [𝜑, 𝜕, 𝜓] 𝑇
. For analyzing and designing of torpedo control system,
it is common to study the motion of torpedo in three separately channel, i.e. horizontal, vertical
and roll damping channel. The external force have an effect on torpedo are defined by
𝜏 𝑅𝐵 = 𝑀𝐴 𝑣̇ + 𝐶𝐴(𝑣)𝑣 + 𝐷(𝑣)𝑣 + 𝐿(𝑣)𝑣 + 𝑔(𝜂) + 𝜏 (2)
where 𝑀𝐴, 𝐶𝐴(𝑣) is the inertia matrix and the centrifugal Coriolis matrix; 𝐷(𝑣) is the matrix of
hydrodynamic damping terms; 𝑔(𝜂) is the vector of gravity and buoyant forces; 𝐿(𝑣) is a force
matrix and rudder torque parameters; 𝜏 = 𝜏 𝑟 + 𝜏𝑓 is the control-input vector describing the
efforts acting on the torpedo include the rudder, the fins and the propeller. The torpedo motion
is given by
𝑀 𝑅𝐵 𝑣̇ + 𝐶 𝑅𝐵(𝑣)𝑣 = 𝜏 𝑅𝐵 (3)
where 𝑀 𝑅𝐵 is the matrix of inertia; 𝐶 𝑅𝐵 is the matrix of centrifugal coriolis; 𝜏 𝑅𝐵 is an external force
vector which acts on the torpedo body. In the six-degree coordinate system, the torpedo motion
equations are represented as follows:

3. TELKOMNIKA ISSN: 1693-6930 
Control for Torpedo Motion Based on Fuzzy-PSO Advantage Technical (Viet-Dung Do)
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{
𝑥̇ = 𝑢0 𝑐𝑜𝑠𝜓𝑐𝑜𝑠𝜕 + 𝑣(𝑐𝑜𝑠𝜓𝑠𝑖𝑛𝜕𝑠𝑖𝑛𝜑 − 𝑠𝑖𝑛𝜓𝑐𝑜𝑠𝜑) + 𝑤(𝑐𝑜𝑠𝜓𝑠𝑖𝑛𝜕𝑐𝑜𝑠𝜑 + 𝑠𝑖𝑛𝜓𝑠𝑖𝑛𝜑)
𝑦̇ = 𝑢0 𝑠𝑖𝑛𝜓𝑐𝑜𝑠𝜕 + 𝑣(𝑠𝑖𝑛𝜓𝑠𝑖𝑛𝜕𝑠𝑖𝑛𝜑 + cos𝜓𝑐𝑜𝑠𝜑) + 𝑤(sin𝜓𝑠𝑖𝑛𝜕𝑐𝑜𝑠𝜑 − cos𝜓𝑠𝑖𝑛𝜑)
𝑧̇ = −𝑢0 𝑠𝑖𝑛𝜕 + 𝑣𝑐𝑜𝑠𝜕𝑠𝑖𝑛𝜑 + 𝑤𝑐𝑜𝑠𝜕𝑐𝑜𝑠𝜑
𝜑̇ = 𝑃 + 𝑞𝑡𝑎𝑛𝜕𝑠𝑖𝑛𝜑 + 𝑟𝑡𝑎𝑛𝜕𝑐𝑜𝑠𝜑
𝜕̇ = 𝑞𝑐𝑜𝑠𝜑 − 𝑟𝑠𝑖𝑛𝜑
𝜓̇ = 𝑞𝑠𝑒𝑐𝜕𝑠𝑖𝑛𝜑 + 𝑟𝑠𝑒𝑐𝜕𝑐𝑜𝑠𝜑
(4)
In order to control the torpedo object, it is necessary to transform the torpedo
dynamics (4) to form the MIMO [8] nonlinear system with quadratic equation written as
𝑦1 = 𝑓1(𝑥) + ∑ 𝑔1𝑗(𝑥)
1
𝑗=1
𝑢𝑗 + 𝑑1; 𝑦2 = 𝑓2(𝑥) + ∑ 𝑔2𝑗(𝑥)
2
𝑗=2
𝑢𝑗 + 𝑑2; 𝑦3
= 𝑓3(𝑥) + ∑ 𝑔3𝑗(𝑥)
3
𝑗=3
𝑢𝑗 + 𝑑3
(5)
where 𝑢 = [𝑢1, 𝑢2, 𝑢3] 𝑇
∈ 𝑅3
are the control inputs which include the rudder angle, diving plane
angle and fin shake reduction. 𝑦 = [𝑦1, 𝑦2, 𝑦3] 𝑇
∈ 𝑅3
are system outputs, including yaw horizontal,
the depth vertical and roll damping. 𝑑 = [𝑑1, 𝑑2, 𝑑3] 𝑇
∈ 𝑅3
are external disturbances, 𝑓𝑘(𝑥) and
𝑔 𝑘𝑗(𝑥) are smooth nonlinear functions with 𝑘 = 1 ÷ 3.
3. Fuzzy-PSO Controller Design
3.1. Particle Swarm Optimization
A population consisting of particle is put into the n-dimensional search space with
randomly chosen velocities and the initial location of particles [9, 10]. The population of particles
is expected to have high tendency to move in high dimensional search spaces in order for
detecting better solution [11]. If the certain particle finds out the better solution than the previous
solution, the other will move to be near this location [12]. The process is repeated for the
next position. The population size is denoted by 𝑠, each particle 𝑖 (1 ≤ 𝑖 ≤ 𝑠) presents a test
solution with parameters 𝑗 = 1,2, . . , 𝑛. At the 𝑘 generation, position of each particle is located
by 𝑝𝑖(𝑘), the current speed of particle is 𝑣𝑖(𝑘), and the best location is 𝑃𝑏𝑖(𝑘). The best particle
among all population is represented by 𝐺𝑏(𝑘). The particles of population update the attributes
then each generation [13]. Updating property will be realize according to (6) as
𝑣𝑖,𝑗(𝑘 + 1) = 𝑤(𝑘)𝑣𝑖,𝑗(𝑘) + 𝑐1 𝑟1[𝑃𝑏𝑖,𝑗(𝑘) − 𝑝𝑖,𝑗(𝑘)] + 𝑐2 𝑟2[𝐺𝑏𝑗(𝑘) − 𝑝𝑖,𝑗(𝑘)] (6)
where 𝑤 is the inertia weight, 𝑐1 and 𝑐2 are acceleration coefficient, 𝑟1 and 𝑟2 are random
constants in the range (0.1), 𝑔 is the number of repetitions [14]. The inertia weights are updated
according to (7) as
𝑤(𝑔) =
(𝑖𝑡𝑒𝑟 𝑚𝑎𝑥 − 𝑔)(𝑤 𝑚𝑎𝑥 − 𝑤 𝑚𝑖𝑛)
𝑖𝑡𝑒𝑟 𝑚𝑎𝑥
+ 𝑤 𝑚𝑖𝑛 (7)
where 𝑖𝑡𝑒𝑟 𝑚𝑎𝑥 is the maximum value of multiple loop, 𝑤 𝑚𝑎𝑥 is respectively the largest of inertial
weightsand, 𝑤 𝑚𝑖𝑛 are respectively the smallest of inertial weights. The new position of particle
can be updated by (8) as follows:
𝑝𝑖,𝑗(𝑔 + 1) = 𝑝𝑖,𝑗(𝑔) + 𝑣𝑖,𝑗(𝑔 + 1) (8)
the best position of each particle can be updated by
𝑃𝑏𝑖,𝑗(𝑔 + 1) = {
𝑃𝑏𝑖,𝑗(𝑔), 𝑖𝑓 𝐽 (𝑝𝑖,𝑗(𝑔 + 1)) ≥ 𝐽 (𝑃𝑏𝑖,𝑗(𝑔))
𝑝𝑖,𝑗(𝑔 + 1), 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
(9)
finally, the best location for the whole group is performed by (10) as

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𝐺𝑏𝑗(𝑔 + 1) = 𝑎𝑟𝑔 𝑚𝑖𝑛 𝑃𝑏 𝑖,𝑗
𝐽( 𝑃𝑏𝑖,𝑗(𝑔 + 1)),1 ≤ 𝑖 ≤ 𝑠 (10)
In order to discover the optimal parameters for fuzzy controller, each variable of the
membership function for Ke(t) and Kde/dt control input is attributed to a particle. So, variables
are initiated randomly in the search space to aim the optimal parameter for the fuzzy controller,
which defines according to the fitness function (minimizing error) [15, 16].
3.2. Fuzzy Controller Design based on Particle Swarm Optimization
We consider the fuzzy modulator which has a double-input, ex(t), dex(t)/d(t) and a
singe-output, u(t). These fuzzy sets are defined as {NB,NS,ZO,PS,PB} correspond to negative
big, negative small, zero, positive small and positive big [17]. The membership function
collections are similarly in Figure 2. And our fuzzy rule are using as in Table 1.
Figure 2. The membership functions are optimized by the PSO algorithm
Table 1. The Synthesis of Composition Rules
uh/us/ur
de/dt
NB NS ZO PS PB
e(t)
NB
NBh
/ NBs
/NBr
NBh
/ NBs
/NBr
NBh
/ NBs
/NBr
NSh
/ NSs
/NSr
ZOh
/ ZOs
/ZOr
NS
NBh
/ NBs
/NBr
NBh
/ NBs
/NBr
NSh
/ NSs
/NSr
ZOh
/ ZOs
/ZOr
PSh
/ PSs
/PSr
ZO
NBh
/ NBs
/NBr
NSh
/ NSs
/NSr
ZOh
/ ZOs
/ZOr
PSh
/ PSs
/PSr
PBh
/ PBs
/PBr
PS
NSh
/ NSs
/NSr
ZOh
/ ZOs
/ZOr
PSh
/ PSs
/PSr
PBh
/ PBs
/PBr
PBh
/ PBs
/PBr
PB
ZOh
/ ZOs
/ZOr
PSh
/ PSs
/PSr
PBh
/ PBs
/PBr
PBh
/ PBs
/PBr
PBh
/ PBs
/PBr
The inference mechanism of Takagi-Sugeno fuzzy method is given by

5. TELKOMNIKA ISSN: 1693-6930 
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𝜇 𝐵(𝑢(𝑡)) = 𝑚𝑎𝑥𝑗=1
𝑚
[𝜇 𝐴1
𝑗 (𝑒(𝑡)), 𝜇 𝐴2
𝑗 (𝑑𝑒(𝑡)), 𝜇 𝐵 𝑗(𝑢(𝑡))] (11)
where 𝜇 𝐴1
𝑗 (𝑒(𝑡)) is the membership functions of error 𝑒(𝑡), 𝜇 𝐴2
𝑗 (𝑑𝑒(𝑡)) is the membership
functions of error velocity 𝑑𝑒/𝑑𝑡. 𝜇 𝐵 𝑗(𝑢(𝑡)) is the membership functions of output response 𝑢(𝑡),
𝑗 is the index of fuzzy set, and 𝑚 is the resulting fuzzy inference [18]. In this paper, we use the
Max-Prod inference rule, the singleton fuzzifier and the centre averaged defuzzifier for
confirming the output response [19]. So the fuzzy output can be expressed as
𝑢(𝑡) =
∑ 𝜇 𝐵(𝑢𝑖(𝑡))𝑢𝑖
𝑚
𝑖=1
∑ 𝜇 𝐵(𝑢𝑖(𝑡))𝑚
𝑖=1
(12)
In order to design the optimal fuzzy controller, the PSO algorithm is applied to discover
optimal parameters for the controller. The process of optimizing parameters consists of three
parts: membership functions correspond to 𝑒(𝑡) fuzzy sets, membership functions correspond to
𝑑𝑒(𝑡) fuzzy sets and membership functions correspond to the output fuzzy sets. Thereby, the
process of optimizing parameters is described as
𝜏 = 𝑃𝑆𝑂[𝜆1 𝜇 𝐴1
𝑗 (𝑒(𝑡)), 𝜆2 𝜇 𝐴2
𝑗 (𝑑𝑒(𝑡)), (𝜆3 + 𝜆41/𝑠)𝜇 𝐵 𝑗(𝑢(𝑡))] (13)
where 𝜆 = [𝜆1, 𝜆2, 𝜆3, 𝜆4] is the parameter adjusting vector which is determined by the PSO. The
different characteristics of fitness function affect how easy or difficult the problem is offered for a
PSO algorithm [20]. The most commonly used fitness function is minimizing the errors, which is
between the output and input signal for the torpedo object. The optimized structure of controller
shows in Figure 3. The fitness function is chosen according to the ITAE criteria [21, 22] as
follows:
𝐼𝑇𝐴𝐸 = ∫ 𝑡
∞
0
|𝑒(𝑡)|𝑑𝑡 (14)
There are three different fuzzy controllers which are designed for the torpedo motion.
The first fuzzy structure is defined by the object characteristic knowledge. The second based on
the PSO algorithms which aim at the optimal range of membership functions. Finally, the
optimal fuzzy controller (FPSO) is designed by the parameters of second fuzzy. The PSO
parameters used for simulation are presented in Table 2.
Table 2. PSO Parameters for Torpedo Simulation
Particles of population 10 Ke and Kde [0.01 0.05]
Loops 30 e1, de1 and u1 [-1 -0.5]
wmax 0.6 e2, de2 and u2 [-1 0]
wmin 0.1 e3, de3 and u3 [-0.5 +0.5]
c1 = c2 1.5 e4, de4 and u4 [0 +1]
Min-offset 200 e5, de5 and u5 [+0.5 +1]
Figure 3. PSO algorithms for torpedo motion optimization

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Figure 4. Adaptive fuzzy-neural for torpedo control system
3.3. Adaptive fuzzy-neural controller design
The advanced adaptive method for torpedo control system (shown as in Figure 4)
presented by V P Pham [5], the state observer given as:
𝑒̂ = 𝐴0 𝑒̂ − 𝐵𝐾𝑐
𝑇
𝑒̂ + 𝐾0(𝐸1 − 𝐸̂1)
𝐸̂1 = 𝐶 𝑇
𝑒̂
(15)
where 𝐾0 = 𝑑𝑖𝑎𝑔[𝐾0, 𝐾0, 𝐾0] ∈ 𝑅6𝑥3
is the gain vector of state observer. Observer error is defined
by: 𝑒̃ = 𝑒 − 𝑒̂ and 𝐸̃1 = 𝑦 + 𝑑 − 𝐸̂1. The fuzzy-neural output is combined 𝑢 𝑓𝑘 and 𝑣, that reduces
disturbance and error for torpedo model. Control signal is express by (16) as
𝑢 = 𝑢 𝑓𝑘 + 𝑣 (16)
where 𝑢 𝑓𝑘 = [𝑢 𝑓𝑘, 𝑢 𝑓𝑘, 𝑢 𝑓𝑘] 𝑇
∈ 𝑅3
, 𝑣 = [𝑣1, 𝑣2, 𝑣3] 𝑇
∈ 𝑅3
. In order to design a Takagi-Sugeno fuzzy
logic with a compact rule base, the rule notation form within 𝐵 𝑘
𝑖
is a binary variable that
determines the consequence of the rule given as
𝑅𝑖 : If 𝑒̂1 is 𝐴 𝑘1
𝑖
…….and 𝑒̂ 𝑛 is 𝐴 𝑘𝑛
𝑖
then 𝑢 𝑓𝑘 is 𝐵 𝑘
𝑖
.
where 𝐴 𝑘1
𝑖
, 𝐴 𝑘2
𝑖
, … 𝐴 𝑘𝑛
𝑖
and 𝐵 𝑘
𝑖
are fuzzy sets. By using the Max-Prod inference rule, the singleton
fuzzifier and the centre averaged defuzzifier [23]. The fuzzy output can be expressed as
bellows:
𝑢 𝑓𝑘 =
∑ 𝜃 𝑘
−𝑖ℎ
𝑖=1 [∏ 𝜇 𝐴 𝑘𝑗
𝑖 (𝑒̂𝑗)]𝑛
𝑗=1
∑ [∏ 𝜇 𝐴 𝑘𝑗
𝑖 (𝑒̂𝑗)]𝑛
𝑗=1
ℎ
𝑖=1
= 𝜃 𝑘
𝑇
𝜑 𝑘(𝑒̂) (17)
For 𝜇 𝐴 𝑘𝑗
𝑖 (𝑒̂𝑗) is the membership function, ℎ is the total number of the If-Then rules, 𝜃 𝑘
−𝑖
is the
point at which 𝜇 𝐵 𝑘
𝑖 (𝜃 𝑘
−𝑖
) = 1, 𝜑 𝑘(𝑒̂) = [𝜑 𝑘
1
, 𝜑 𝑘
2
, … , 𝜑 𝑘
ℎ
] 𝑇
∈ 𝑅ℎ
fuzzy vector [24] with 𝜑 𝑘
𝑖
is defined as
𝜑 𝑘
𝑖
(𝑒̂) =
∏ 𝜇
𝐴 𝑘𝑗
𝑖 (𝑒̂ 𝑗)]𝑛
𝑗=1
∑ [∏ 𝜇
𝐴 𝑘𝑗
𝑖 (𝑒̂ 𝑗)]𝑛
𝑗=1
ℎ
𝑖=1
(where 𝑖 = 1 ÷ ℎ) (18)
The online update law is given by

7. TELKOMNIKA ISSN: 1693-6930 
Control for Torpedo Motion Based on Fuzzy-PSO Advantage Technical (Viet-Dung Do)
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𝜃̇ 𝑘 =
{
𝛾 𝑘 𝐸̃1𝑘∅ 𝑘(𝑒̂) 𝑖𝑓‖𝜃 𝑘‖ < 𝑚 𝜃 𝑘
𝑜𝑟 (‖𝜃 𝑘‖ = 𝑚 𝜃 𝑘
𝑎𝑛𝑑𝐸̃1𝑘 𝜃 𝑘
𝑇
∅ 𝑘 ≥ 0
𝑃𝑟 (𝛾 𝑘 𝐸̃1𝑘∅(𝑒̂)) 𝑖𝑓‖𝜃 𝑘‖ = 𝑚 𝜃 𝑘
𝑎𝑛𝑑𝐸̃1𝑘 𝜃 𝑘
𝑇
∅ 𝑘 < 0
(19)
with 𝛾 𝑘 > 0 is the design adaptive parameter. If ‖𝜃 𝑘‖ < 𝑚 𝜃 𝑘
and ‖𝜃̃ 𝑘‖ < 2𝑚 𝜃 𝑘
, the (19) will be
rewritten as follows:
𝑃𝑟 (𝛾 𝑘 𝐸̃1𝑘∅(𝑒̂)) = 𝛾 𝑘 𝐸̃1𝑘∅ 𝑘(𝑒̂) − 𝛾 𝑘
𝐸̃1𝑘 𝜃 𝑘
𝑇
∅ 𝑘(𝑒̂)
‖𝜃 𝑘‖2
𝜃 𝑘 (20)
where ∅ 𝑘 is updated by the update law (19), then the reducing erroneous (𝑣 𝑘 and 𝛼 𝑘) is a
positive parameter [25] which is expressed by (21) as
𝑣 𝑘 = {
𝜌 𝑘 𝑖𝑓 𝐸̃1𝑘 ≥ 0 𝑎𝑛𝑑 |𝐸̃1𝑘| > 𝛼 𝑘
−𝜌 𝑘 𝑖𝑓 𝐸̃1𝑘 < 0 𝑎𝑛𝑑 |𝐸̃1𝑘| > 𝛼 𝑘
𝜌 𝑘 𝐸̃1𝑘/𝛼 𝑘 𝑖𝑓 |𝐸̃1𝑘| > 𝛼 𝑘
(21)
The adaptive fuzzy-neural control (AFN): The torpedo dynamics are expressed by (5). The
feedback gains are chosen as follows:
a) 𝐾0ℎ
𝑇
= [45 60]; 𝐾𝑐ℎ
𝑇
= [66 4]; 𝐾0𝑠
𝑇
= [26 290]; 𝐾𝑐𝑠
𝑇
= [640 360]; 𝐾0𝑟
𝑇
= [130 240]; 𝐾𝑐𝑟
𝑇
=
[240 130];
b) Reducing erronous parameters are selected as: 𝜌ℎ = 0.4, 𝜌𝑠 = 0.5𝑝𝑖, 𝜌 𝑟 = 10, 𝛼ℎ = 0.001,
𝛼 𝑠 = 0.1 and 𝛼 𝑟 = 0.01.
c) The coefficients of adaptive law are given by: 𝛾ℎ = 100𝑝𝑖, 𝛾𝑠 = 25𝑝𝑖 and 𝛾𝑟 = 2.
d) Current velocity: 𝑣𝑐 = 0.2 𝑚/𝑠, rotation frequence of current: 𝑤𝑐 = 0.2 𝑚/𝑠.
4. Results and discussion
The presented torpedo control system is carried out by proposed FPSO advanced
control technique in section 2. The results of simulation process is described in Figure 5. At the
time 0s and 40s, the torpedo moves from 0m depth to 12 m depth and 24 m depth, the roll
motion of torpedo is fluctuated by current impact. Applying FPSO algorithm to control the
torpedo motion, the torpedo response (yaw horizontal) has good dynamic and static
performance in different initial conditions of entering sea. The optimal control signal makes the
rudder angle yaw, and the fin shake reduction to be accurately. As a result, it helps the torpedo
quickly follow the desired trajectory. At the time 100s, the torpedo horizontal switch from 45
degree to -45 degree, the torpedo depth vertical and roll damping are significantly affected. As
expected, the results show that the proposed method outperforms technical on its effectiveness
and efficiency. The torpedo motion in 3D space (described in Figure 6 and Figure 7) expressed
the stable characteristic of system when the depth object switches over distance, corresponding
change in yaw horizontal. The result of propose controller has strong adaptability and
achieves better control performance for all cases. In the other hand, the response of diving
plane angle plays slowing down process, but it seems appropriate the physical nature of
torpedo.

8.  ISSN: 1693-6930
TELKOMNIKA Vol. 16, No. 6, December 2018: 2999-3007
3006
a. Yaw horizontal b. Depth vertical
c. Roll damping
Figure 5. To compare the simulation responses of Torpedo control system in case of using
proposed FPSO controller (blue) with AFN controller (red) (continue)
Figure 6. Torpedo motion in 3D space with
adaptive fuzzy-neural control
Figure 7. Torpedo motion in 3D space with
proposed FPSO control
5. Conclusions
In this paper, the proposed FPSO controller has been developed for the torpedo motion.
Our proposed control scheme improves the torpedo motion quality, while guaranteeing the
parameters of fuzzy controller in the optimal case. Calibrating control structure of fuzzy system
was intuitive to perform. Its optimal to variations in its displacement and the changing
conditions. Besides, simulation results and simulation comparisons on a torpedo model have
confirmed the effectiveness of the proposed control scheme and its robustness against
nonlinear characteristic. However, the restriction of studies only explore the factors that cause
erroneous is current. In the future work, this study can be extended by examining the other
influences such as seawater viscosity to improve the optimizing accuracy of controller structure.

9. TELKOMNIKA ISSN: 1693-6930 
Control for Torpedo Motion Based on Fuzzy-PSO Advantage Technical (Viet-Dung Do)
3007
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